Rigid Body Statics

1.4 An Overview of Forces

In engineering mechanics, forces acting on bodies are systematically classified according to various criteria. This classification facilitates the analysis and description of force effects and enables engineers to solve engineering problems more efficiently.

After all, there is not just one kind of force. No, there are different types of forces, each acting in its own unique way.

We can neatly sort forces into different categories. Think of them as the drawers of physics. But don't worry, it's not as complicated as it sounds.

There are various ways to classify forces according to their properties:

1. Classification According to Spatial Distribution
   • Point force: A mighty blow that acts only on a single point, like a nail being driven into a wall. Remember: These are idealized representations of forces that do not actually exist in reality.
   • Line force: The cutting edge of your knife, which acts with force along a line. Remember: Again, these are idealized representations of forces that do not actually exist in reality.
   • Surface force: The pressure of your feet on the ground, which is distributed over an area.
   • Volume force: The force of gravity, which acts on every atom in your body.
2. Classification According to Cause
   • Impressed forces:
     • Act on a system from the outside.
     • Are not caused by the system itself.
     • Examples:
       • Weight force
       • Wind force
       • Force from a spring
     • Properties:
       • Independent of the system.
       • Can be caused by other systems or by the environment.
       • Can be constant or time-dependent.
   • Reaction forces:
     • Are counter-forces to the impressed forces. They always act in pairs in opposite directions.
     • Arise from the constraints to which the system is subjected.
     • Examples:
       • Normal force of a support surface
       • Friction force
       • Bearing force
     • Properties:
       • Dependent on the system.
       • Determined by the contact surfaces and the material properties of the systems.
       • Can be static or dynamic.

   Important:

   • Impressed forces and reaction forces are always in equilibrium.
   • Reaction forces restrict the freedom of movement (degrees of freedom) of a body.
   • To completely describe the force action on a system, both the impressed forces and the reaction forces must be considered.

   Example:

   • A book is lying on a table.
     • Impressed force: Weight force of the book (directed downwards)
     • Reaction force: Normal force of the table (directed upwards)
3. Classification According to the Range of Action
   • Near forces:
     • Only act between two bodies that are in contact with each other.
     • Examples:
       • Normal force
       • Friction force
       • Adhesive force
       • Spring force
     • Properties:
       • Always act in pairs in opposite directions.
       • Dependent on the contact area and the material properties of the bodies.
       • Decrease rapidly with the distance between the bodies.
   • Far forces:
     • Also act between bodies that are not in contact with each other.
     • Examples:
       • Gravitational force between two masses
       • Electric force
       • Magnetic force
     • Properties:
       • Act over any distance.
       • Dependent on the mass or charge of the bodies.
       • Decrease with the distance between the bodies, but usually more slowly than near forces.

   Important:

   The distinction between near and far forces is important for the analysis and modeling of mechanical systems. In some cases, near forces can be neglected if the far forces dominate.

   Example:

   • When calculating the flight path of an airplane, the gravitational force is the dominant force, and the near forces such as air friction can initially be neglected.
4. Classification According to the Point of Action
   • External forces:
     • Loads on the system (cf. impressed forces):
       • Act on the system from the outside and are caused by other systems or the environment.
       • Examples:
         • Weight force
         • Wind force
         • Force from a spring
     • Reaction forces at the system boundary: (cf. reaction forces):
       • Are counter-forces to the external loads and arise from the constraints at the system boundary.
       • Examples:
         • Normal force of a support surface
         • Friction force
         • Bearing force
   • Internal forces:
     • Forces that act within a system:
       • Are interactions between the individual parts of the system.
       • Can be made visible by the method of sections.
       • Examples:
         • Tension in a rope
         • Pressure in a fluid

• A beam resting on two supports:

  

  • Support forces F_A and F_B:
    • Classification according to spatial distribution: Point force as an idealization.
    • Classification according to cause: Reaction force, since it is the normal force at the support point. It arises from the constraint that the system (beam) rests here.
    • Classification according to the range of action: Near force, since it acts between two bodies that are in contact with each other (beam and support).
    • Classification according to the point of action: External force, since it is a reaction force at the outer boundary of the system (beam).
  • Weight force G:
    • Classification according to spatial distribution: Volume force (gravity).
    • Classification according to cause: Impressed force, since it acts on the beam system from the outside. It is not caused by the system itself.
    • Classification according to the range of action: Far force, since it acts as a gravitational force between two masses between bodies that are not in contact with each other.
    • Classification according to the point of action: External force, since it acts as an impressed force from outside on the beam system.